Category Archives: recursion

Post without words #3

Posted on October 29, 2011 by Brent

(This is my 200th post! =)

Posted in counting, pattern, pictures, posts without words, recursion | 11 Comments

The hyperbinary sequence and the Calkin-Wilf tree

Posted on October 18, 2009 by Brent

And now, the amazing conclusion to this series of posts on Neil Calkin and Herbert Wilf’s paper, Recounting the Rationals, and the answers to all the questions about the hyperbinary sequence. Hold on to your hats! The Calkin-Wilf Tree First, … Continue reading →

Posted in arithmetic, computation, induction, iteration, number theory, pattern, proof, recursion, sequences, solutions | Tagged , , , , , , | 6 Comments

More hyperbinary fun

Posted on September 28, 2009 by Brent

When I originally posed Challenge #12, a certain Dave posted a series of comments with some explorations and partial solutions to part II (the hyperbinary sequence). Although I gave the “solution” in my last post, no solution to any problem … Continue reading →

Posted in challenges, induction, pattern, proof, recursion, sequences, solutions | Tagged , | 12 Comments

Challenge #12 solution, part III

Posted on April 24, 2008 by Brent

And now for the solution to problem #3 from Challenge #12, which asked: how many ways are there to write a positive integer n as a sum of powers of two, with no restrictions on how many powers of two … Continue reading →

Posted in counting, pattern, recursion, sequences, solutions | 1 Comment

Recounting the Rationals, part III

Posted on January 24, 2008 by Brent

First, a quick recap: continuing an exposition of the paper Recounting the Rationals, we’re investigating the tree of fractions shown below (known as the Calkin-Wilf tree), which is constructed by placing 1/1 at the root node, and giving each node … Continue reading →

Posted in number theory, pattern, proof, recursion | 10 Comments

Recounting the Rationals, part II (fractions grow on trees!)

Posted on January 7, 2008 by Brent

Today I’d like to continue my exposition of the paper “Recounting the Rationals”, which I introduced in a previous post. Recall that our goal is to come up with a “nice” list of the positive rational numbers — where by … Continue reading →

Posted in infinity, number theory, pattern, recursion, sequences | 22 Comments